<h2>Problem 94</h2>
<div style="color:#666;font-size:80%;">29 April 2005</div><br />
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<p>It is easily proved that no equilateral triangle exists with integral length sides and integral area. However, the <i>almost equilateral triangle</i> 5-5-6 has an area of 12 square units.</p>
<p>We shall define an <i>almost equilateral triangle</i> to be a triangle for which two sides are equal and the third differs by no more than one unit.</p>
<p>Find the sum of the perimeters of all <i>almost equilateral triangles</i> with integral side lengths and area and whose perimeters do not exceed one billion (1,000,000,000).</p>

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